Space-Time Block Coding Systems and Methods

ABSTRACT

Although orthonormal space-time coding matrices provide for optimal communication system performance in that associated correlation matrices include no non-zero off-diagonal elements, unity code rate orthonormal coding matrices are difficult to identify for arbitrary communication network equipment. According to embodiments of the present invention, non-orthonormal space-time coding matrices, for which associated correlation matrices include non-zero off-diagonal elements, are used to encode data symbols. The non-orthonormal space-time coding matrices are more easily determined, and undesirable effects of the non-zero off-diagonal components are reduced by selecting a coding matrix from among a number of such matrices. For example, a particular space-time coding matrix may be selected from a number of generated space-time coding matrices based on a number of non-zero off-diagonal elements or a power of a trace of the associated correlation matrices.

RELATED APPLICATION

This application is a continuation of application Ser. No. 11/547,187filed Apr. 1, 2004 which is hereby incorporated by reference in itsentirety.

FIELD OF THE INVENTION

This invention relates generally to communications and, in particular,to space-time coding of communication signals.

BACKGROUND

Space-Time Transmit Diversity (MD) coding for two transmitting antennashas been adopted in many new wireless communication standards including3GPP (3^(rd) Generation Partnership Project), 3GPP2, and IEEE (Instituteof Electrical and Electronics Engineers) 802.16, for example. It hasbeen shown that so-called Alamouti codes for two antennas achievemaximum diversity gain for two transmit antennas and unity coding rate.

Numerous attempts have subsequently been made to search for space-timecodes that achieve the maximum diversity gain with unity code rate formore than two antennas.

On the other hand, several studies on the combining of STTD and OTD(Orthonormal Transmit Diversity) have also been carried out. One primarydifficulty associated with such coding schemes is that orthonormalcomplex matrices, which provide for optimal signal reception, have notbeen found for arbitrary numbers of transmit antennas. Although thesecombined codes possess simple encoding and decoding algorithms, in theabsence of arbitrary-size orthonormal matrices, ad-hoc design of suchcodes is required, and results in sub-optimal performance.

One desirable aspect of STTD techniques is their applicability to singleantenna receivers. Key advantages of STTD include maximum diversity gainand relatively simple decoding at a receiver involving only complexmultiplications. In addition, while STTD is a complementary codingtechnique to MIMO (Multiple Input Multiple Output) BLAST, STTD does notrequire that the number of transmit antennas be less than the number ofreceive antennas across a communication network.

Therefore, although space-time techniques may provide advantages incommunication systems, there are no currently known techniques thatexhibit unity code rate and maximum transmit diversity gain for morethan two transmit antennas.

SUMMARY OF THE INVENTION

According to an aspect of the invention, multiple space-time codingmatrices are determined, each having a respective associated correlationmatrix. Each correlation matrix includes non-zero off-diagonal elements.One of the space-time coding matrices for which the associatedcorrelation matrix has a least number of non-zero off-diagonal elementsis selected and used to encode data symbols.

The selected space-time coding matrix may include rows respectivelycorresponding to transmit antennas and columns respectivelycorresponding to time slots in which the data symbols are to betransmitted.

In one embodiment, the selected space-time coding matrix is punctured,and the data symbols are encoded using the punctured selected space-timecoding matrix. The puncturing may be according to either a fixed or anadaptive puncturing ratio.

A phase rotation factor may also be determined and applied to theencoded data symbols. The phase rotation factor is preferably determinedto reduce values of the off-diagonal elements of the correlation matrixassociated with the selected space-time coding matrix. In a closed loopsystem, the phase rotation factor or feedback information from which thephase rotation factor is calculated may be received from a receiver towhich the data symbols are to be transmitted.

A related receiving method is also provided, and preferably includesreceiving and decoding data symbols in a communication signal. The datasymbols have been encoded using a space-time coding matrix selected fromspace-time coding matrices having respective associated correlationmatrices which have non-zero off-diagonal elements. The associatedcorrelation matrix for the selected space-time coding matrix has a leastnumber of non-zero off-diagonal elements.

In another aspect, the invention provides a method which includeddetermining multiple space-time coding matrices having respectiveassociated correlation matrices, selecting one of the space-time codingmatrices for which a trace of the associated correlation matrix has amaximum power, and encoding data symbols using the selected space-timecoding matrix.

A receiving method is also provided, and includes receiving and decodingdata symbols in a communication signal, the data symbols having beenencoded using a space-time coding matrix selected from space-time codingmatrices having respective associated correlation matrices, a trace ofthe associated correlation matrix for the selected space-time codingmatrix having a maximum power.

A system according to another aspect of the invention includes an inputand a processor. The input is configured to receive data symbols, andthe processor is configured to determine multiple space-time codingmatrices, each having a respective associated correlation matrix whichhas non-zero off-diagonal elements, to select one of the space-timecoding matrices for which the associated correlation matrix has a leastnumber of non-zero off-diagonal elements, and to encode the data symbolsusing the selected space-time coding matrix.

In a still further aspect, the invention also provides a system havingan input configured to receive, in a communication signal, data symbolsencoded using a space-time coding matrix selected from multiplespace-time coding matrices having respective associated correlationmatrices which have a plurality of non-zero off-diagonal elements, theassociated correlation matrix for the selected space-time coding matrixhaving a least number of non-zero off-diagonal elements, and a processorconfigured to decode the encoded data symbols.

A system according to another aspect of the invention includes an inputconfigured to receive data symbols and a processor. The processor isconfigured to determine a number of space-time coding matrices, eachhaving a respective associated correlation matrix, to select one of thespace-time coding matrices for which a trace of the associatedcorrelation matrix has a maximum power, and to encode data symbols usingthe selected space-time coding matrix.

A related receiving system includes an input configured to receive datasymbols in a communication signal and a processor configured to decodethe encoded data symbols. The received data symbols have been encodedusing a space-time coding matrix selected from space-time codingmatrices having respective associated correlation matrices, a trace ofthe associated correlation matrix for the selected space-time codingmatrix having a maximum power.

There is also provided, in yet another aspect, a method in which datasymbols are input and encoded. The data symbols are encoded using aspace-time coding matrix selected from a number of space-time codingmatrices having respective associated correlation matrices. Thecorrelation matrices have non-zero off-diagonal elements, and theassociated correlation matrix for the selected space-time coding matrixhas a least number of non-zero off-diagonal elements.

Other aspects and features of embodiments of the present invention willbecome apparent to those ordinarily skilled in the art upon review ofthe following description of specific embodiments of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

Examples of embodiments of the invention will now be described ingreater detail with reference to the accompanying diagrams, in which:

FIG. 1 is a block diagram of a system in accordance with an embodimentof the invention;

FIG. 2 is a flow diagram illustrating a method according to anembodiment of the invention;

FIG. 3 is a plot of FER (Frame Error Rate) versus Eb/No (Energy per Bitto Spectral Noise Density ratio) for simulations of embodiments of theinvention and an example 4×2 communication scheme;

FIG. 4 is a plot of FER versus Eb/No for simulations of embodiments ofthe invention and an example 4×1 communication scheme;

FIG. 5 is a plot of FER versus Eb/No for simulations of furtherembodiments of the invention and an example 4×1 communication scheme;

FIG. 6 is a block diagram of a closed loop system according to anembodiment of the invention;

FIG. 7 is a flow diagram of a closed loop method according to anembodiment of the invention;

FIG. 8 is a plot of FER versus Eb/No for simulations of closed loopembodiments of the invention and an example conventional closed loopcommunication scheme;

FIG. 9 is a plot of FER versus Eb/No for simulations of open loop andclosed loop embodiments of the invention;

FIG. 10 is a block diagram of an embodiment of the invention adapted fora CDMA (Code Division Multiple Access) communication system; and

FIG. 11 is a block diagram of a further embodiment of the inventionadapted for a CDMA communication system,

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

In a MIMO communication system with a fixed number of antennas at atransmitter, a variable number of antennas at different receivers, andadaptive coding modulation operation, an increase in the number ofreceive antennas can increase the order of modulation and thus increasethe spectral efficiency. For downlink communications in such a system, abase station or other network element would be a transmitter, whereas acommunication terminal or device configured for operation within thecommunication system would be a receiver.

Consider, for example, a system with M transmit antennas and N receiveantennas in a frequency non-selective, slowly fading channel. Thesampled baseband-equivalent channel model is given by Y=HZ+η, (1) whereY ∈ C^(N) is a symbol received at a j^(th) one of the N receiveantennas;

H ∈ C^(N×M) is the complex channel matrix with the (i,j)^(th) elementbeing representative of the complex narrow band Gaussian random processbetween an i^(th) transmit antenna and the j^(th) receive antenna;

Z ∈ C^(M) is a matrix of transmitted symbols, the i^(th) element of Z ∈C^(M) being the symbol transmitted at the i^(th) transmit antenna;

η ∈ C^(N) is additive white Gaussian noise modeled as a zero meancircularly symmetric complex Gaussian random vector with statisticallyindependent elements, that is, η˜N(0,2σ_(η) ²I_(N)), where σ_(η) ² isthe noise variance and I_(N) is an identity matrix of dimension N; andC^(x) is a set of x complex numbers.

As described above, orthonormal space-time coding matrices, alsoreferred to as STBC (Space-Time Block Coding) matrices, for arbitrarynumbers of transmit antennas have not been found. For systems havingmore than 2 transmit antennas, there is a very large set ofnon-orthonormal combinations for such coding. Therefore, a significanttask in defining effective space-time coding is to identify a space-timecoding matrix to achieve the greatest diversity gain in conjunction withchannel coding.

However, it is not feasible to search for the best combinations forspace-time coding by simple exhaustive searching, for example. Theamount of computation required to search all possible coding matricesand then perform simulation such as Monte-Carlo simulation toinvestigate diversity gain tends to be prohibitive, even forcomputer-based searching.

According to an aspect of the present invention, space-time codingmatrix design is based on reducing the cross-correlation in a codingmatrix linear transformation. Such a transformation, with a reducednumber of non-zero correlation coefficients in a correlation matrix, isreferred to herein as Quasi-Orthonormal Space-Time Block Coding(QO-STBC). Although strictly not orthonormal, such coding matricesprovide many of the advantages of orthonormal coding matrices and aremore easily identified by searching, particularly for higher-dimensionalsystems with more than 2 transmit antennas.

FIG. 1 is a block diagram of a system in accordance with an embodimentof the invention. The system of FIG. 1 includes a transmitter 10 and areceiver 22. The transmitter 10 includes a space-time encoder 12connected to a plurality of M antennas 14, 20. The receiver 22 similarlyincludes a plurality of N antennas 24, 26 connected to a decoder 28. Ina preferred embodiment, the transmitter 10 is implemented at a basestation or other network element that supports wireless communicationswith communication terminals, and the receiver 10 is implemented at oneor more communication terminals. The encoder 12, the decoder 28, andpossibly other components of the transmitter 10 and the receiver 22 maybe provided, for example, by a dedicated processor such as a DSP(digital signal processor) or a general-purpose processor which executesnot only signal processing software, but also other software such asoperating system software or software applications.

It should be appreciated that the system of FIG. 1 is intended forillustrative purposes only. Embodiments of the invention may beimplemented in conjunction with systems having fewer, further, ordifferent components than those shown in FIG. 1. For example, as will beapparent to those skilled in the art to which the present inventionpertains, a transmitter may include further components in addition tothe encoder 12 and the antennas 14, 20, such as components to receive orprocess symbols for transmission, to determine or store coding matrices,or to store or otherwise process encoded symbols output by the encoder12 prior to transmission. Similarly, a receiver may include componentsto further process received signals decoded by the decoder 28. Also,although two antennas 24, 26 are shown in the receiver 22, the inventionis in no way dependent upon multiple receive antennas. A receiver mayhave one or more antennas. In addition, communication equipment at whichthe transmitter 10 and the receiver 22 are implemented normally supportboth transmit and receive operations.

As will become apparent from the following description, the encoder 12encodes symbols, illustratively modulation symbols such as QPSK(Quadrature Phase Shift Keying) or QAM (Quadrature Amplitude Modulation)symbols, using a coding matrix. Encoded symbols transmitted via theantennas 14, 20 and received by the receiver 22 are decoded by thedecoder 28.

Let F(S) denote a matrix of space-time encoded symbols at the output ofthe encoder 12 for a 2M-dimensional vector of complex input symbolsS=[s_(1,r), s_(1,i), s_(2,r), s_(2,i), . . . , s_(M,r)s_(M,i)]^(T),where the subscripts r and i denote real and imaginary components of acomplex symbol, respectively. F(S) is then a matrix with 2M×2Mdimension. From equation (1), a signal received at a receiver,neglecting noise for convenience, can be written as

$\begin{matrix}{{\begin{bmatrix}y_{1,1,r} & \ldots & y_{1,M,r} \\y_{1,1,i} & \ldots & y_{1,M,i} \\\ldots & \ldots & \ldots \\y_{N,1,r} & \ldots & y_{N,M,r} \\y_{N,1,i} & \ldots & y_{N,M,i}\end{bmatrix} = {\begin{bmatrix}h_{1,1,r} & {- h_{1,1,i}} & \ldots & h_{M,1,r} & {- h_{M,1,i}} \\h_{1,1,i} & h_{1,1,r} & \ldots & h_{M,1,i} & h_{m,1,r} \\\ldots & \ldots & \ddots & \ldots & \ldots \\h_{1,N,r} & {- h_{1,N,i}} & \ldots & h_{M,N,r} & {- h_{M,N,i}} \\h_{1,N,i} & h_{1,N,r} & \ldots & h_{M,N,i} & h_{M,N,r}\end{bmatrix}{F(S)}}},} & (2)\end{matrix}$

where y_(n,m,r), y_(n,m,i) are real and imaginary components of acomplex sample observed at an n^(th) receiving antenna in an m^(th) timeinstant; and are real and imaginary parts of channel gain from an m^(th)transmitting antenna to the n^(th) receiving antenna.

For a 4×1 antenna configuration with M=4 and N=1, equation (2) can beexpressed as

$\begin{matrix}{{\begin{bmatrix}y_{1,r} & \ldots & y_{4,r} \\y_{1,i} & \ldots & y_{4,i}\end{bmatrix} = {{\begin{bmatrix}h_{1,r} & {- h_{1,i}} & \ldots & h_{4,r} & {- h_{4,i}} \\h_{1,i} & h_{1,r} & \ldots & h_{4,i} & h_{4,r}\end{bmatrix}{F(S)}} = {{HF}(S)}}}\mspace{79mu} {where}\mspace{79mu} {H = \begin{bmatrix}h_{1,r} & {- h_{1,i}} & \ldots & h_{4,r} & {- h_{4,i}} \\h_{1,i} & h_{1,r} & \ldots & h_{4,i} & h_{4,r}\end{bmatrix}}} & (3)\end{matrix}$

is 2×2M=2×8 matrix of channel gain factors.

In the case of linear STBC, each column of F(S) is a linear combinationof components of the S vector. Equation (3) can then be written as

$\begin{matrix}{{Y = {\begin{bmatrix}y_{1,r} \\y_{1,i} \\\ldots \\y_{M,r} \\y_{M,i}\end{bmatrix} = {{\begin{bmatrix}{HF}_{1} \\\ldots \\{HF}_{M}\end{bmatrix}S} \equiv {{\Phi (H)}S}}}},} & (4)\end{matrix}$

where F_(m) is a 2M×2M matrix of a linear transformation of the S vectorin an m^(th) column of the F(S) matrix.

Taking into account the STBC and the transmitted signal, there exists alinear transformation of the Φ(H)S vector of symbols. The performance ofthis transformation will depend on the characteristics of the codingmatrix. Therefore, according to an aspect of the invention, a codingmatrix search criterion is based on the correlation matrix of such alinear transformation. From equation (4), the correlation matrix may bedefined as

$\begin{matrix}{R = {{{\Phi (H)}^{T}{\Phi (H)}} = {\sum\limits_{m = 1}^{M}\; {F_{m}^{T}H^{T}{{HF}_{m}.}}}}} & (5)\end{matrix}$

In one embodiment, the number of non-zero correlation coefficients inthe correlation matrix is reduced, and preferably minimized. Accordingto a preferred embodiment, unity code rate coding matrices, wherein anumber of symbols are transmitted in an equal number of time slots,represented by columns in a coding matrix, are searched to identify acoding matrix with an associated correlation matrix which possesses aminimum number of non-zero elements. Three such complex matrices withonly 4 pairs of non-zero correlation coefficients in the correspondingcorrelation matrices are listed below.

A first type of space-time coding matrix

$\begin{matrix}{{F^{(1)}(S)} = \begin{bmatrix}s_{1} & {- s_{2}^{*}} & {- s_{3}^{*}} & s_{4} \\s_{2} & s_{1}^{*} & {- s_{4}^{*}} & {- s_{3}} \\s_{3} & {- s_{4}^{*}} & s_{1}^{*} & {- s_{2}} \\s_{4} & s_{3}^{*} & s_{2}^{*} & s_{1}\end{bmatrix}} & (6)\end{matrix}$

has an associated correlation matrix of

$\begin{matrix}{{R^{(1)} = \begin{bmatrix}d & 0 & 0 & 0 & 0 & 0 & {{- 2}a} & 0 \\0 & d & 0 & 0 & 0 & 0 & 0 & {{- 2}a} \\0 & 0 & d & 0 & {2a} & 0 & 0 & 0 \\0 & 0 & 0 & d & 0 & {2a} & 0 & 0 \\0 & 0 & {2a} & 0 & d & 0 & 0 & 0 \\0 & 0 & 0 & {2a} & 0 & d & 0 & 0 \\{{- 2}a} & 0 & 0 & 0 & 0 & 0 & d & 0 \\0 & {{- 2}a} & 0 & 0 & 0 & 0 & 0 & d\end{bmatrix}},} & (7)\end{matrix}$

where the * operator indicates a complex conjugate; a=Re{h₂h₃*−h₁h₄*};and

$d = {{\sum\limits_{m = 1}^{M}\; \left( {h_{m,r}^{2} + h_{m,i}^{2}} \right)} = {\sum\limits_{m = 1}^{M}\; {{h_{m}}^{2}.}}}$

A second type of coding matrix

$\begin{matrix}{{F^{(2)}(S)} = \begin{bmatrix}s_{1} & {- s_{3}^{*}} & {- s_{4}^{*}} & s_{2} \\s_{2} & s_{4}^{*} & s_{3}^{*} & s_{1} \\s_{3} & s_{1}^{*} & {- s_{2}^{*}} & {- s_{4}} \\s_{4} & {- s_{2}^{*}} & s_{1}^{*} & {- s_{3}}\end{bmatrix}} & (8)\end{matrix}$

has an associated correlation matrix of

$\begin{matrix}{{R^{(2)} = \begin{bmatrix}d & 0 & {2b} & 0 & 0 & 0 & 0 & 0 \\0 & d & 0 & {2b} & 0 & 0 & 0 & 0 \\{2b} & 0 & d & 0 & 0 & 0 & 0 & 0 \\0 & {2b} & 0 & d & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & d & 0 & {{- 2}b} & 0 \\0 & 0 & 0 & 0 & 0 & d & 0 & {{- 2}b} \\0 & 0 & 0 & 0 & {{- 2}b} & 0 & d & 0 \\0 & 0 & 0 & 0 & 0 & {{- 2}b} & 0 & d\end{bmatrix}},{{{where}\mspace{14mu} b} = {{Re}{\left\{ {{h_{1}h_{2}^{*}} - {h_{3}h_{4}^{*}}} \right\}.}}}} & (9)\end{matrix}$

For a third type of coding matrix

$\begin{matrix}{{{F^{(3)}(S)} = \begin{bmatrix}s_{1} & {- s_{4}^{*}} & {- s_{2}^{*}} & s_{3} \\s_{2} & {- s_{3}^{*}} & s_{1}^{*} & {- s_{4}} \\s_{3} & s_{2}^{*} & s_{4}^{*} & s_{1} \\s_{4} & s_{1}^{*} & {- s_{3}^{*}} & {- s_{2}}\end{bmatrix}},} & (10)\end{matrix}$

the associated correlation matrix is

$\begin{matrix}{{R^{(3)} = \begin{bmatrix}d & 0 & 0 & 0 & {2c} & 0 & 0 & 0 \\0 & d & 0 & 0 & 0 & {2c} & 0 & 0 \\0 & 0 & d & 0 & 0 & 0 & {2c} & 0 \\0 & 0 & 0 & d & 0 & 0 & 0 & {2c} \\{2c} & 0 & 0 & 0 & d & 0 & 0 & 0 \\0 & {2c} & 0 & 0 & 0 & d & 0 & 0 \\0 & 0 & {2c} & 0 & 0 & 0 & d & 0 \\0 & 0 & 0 & {2c} & 0 & 0 & 0 & d\end{bmatrix}},{{{where}\mspace{14mu} c} = {{Re}{\left\{ {{h_{1}h_{3}^{*}} - {h_{2}h_{4}^{*}}} \right\}.}}}} & (11)\end{matrix}$

It is possible to perform column permutations on the above three complexmatrices, also referred to herein as mother coding matrices, to getanother STBC matrix. However, since such permuted matrices would be oneof these three types of QO-STBC matrices with a reduced number ofnon-zero correlation coefficients, the performance of a permuted matrixwill be the same as that of the corresponding mother coding matrix.

The above mother coding matrices are for the illustrative example of 4×1STTD and block length 4. Extrapolation to other dimensions ofcommunication systems will be apparent to those skilled in the art. Withmore than one receive antenna, for example, correlation matrices havethe same form, but with the following values of the correlationcoefficients:

${a = {\sum\limits_{n = 1}^{N}{{Re}\left\{ {{h_{2,n}h_{3,n}^{*}} - {h_{1,n}h_{4,n}^{*}}} \right\}}}};$${b = {\sum\limits_{n = 1}^{N}{{Re}\left\{ {{h_{1,n}h_{2,n}^{*}} - {h_{3,n}h_{4,n}^{*}}} \right\}}}};$${c = {\sum\limits_{n = 1}^{N}{{Re}\left\{ {{h_{1,n}h_{3,n}^{*}} - {h_{2,n}h_{4,n}^{*}}} \right\}}}};{and}$$d = {\sum\limits_{n = 1}^{N}{\sum\limits_{m = 1}^{M}{{h_{m,n}}^{2}.}}}$

As those skilled in the art will appreciate, these principles may alsobe applied for more than 4 transmit antennas, for which correlationcoefficients may be determined in a similar manner,

Analyzing the correlation matrices in the above table, it is clear thatthere exists only pairwise correlation. For each STBC matrix, thereexists an associated correlation matrix with unique correlationcoefficients. For example, in the first matrix F⁽¹⁾(S) there existscorrelation between symbols s₁, s₄ and s₂, s₃, as indicated by therelative position of diagonal elements and off-diagonal elements in thecorrelation matrix R⁽¹⁾. Similarly, in the second matrix F⁽²⁾(S), thereexists a correlation between symbols s₁, s₂ and s₃, s₄ and, in the thirdmatrix F⁽³⁾(S), there exists a correlation between symbols s₁, s₃ ands₂, s₄. The correlation coefficients for all three matrices not onlyhave different values, but it is also possible to show that these valuesare uncorrelated, i.e.,

E{ab}=E{bc}=E{ac}=0 With these properties, the above QO-STBC matrices,can be concatenated into a longer matrix to form a so-called ExtendedQuasi-Orthonormal Space-Time Block Code (EQO-STBC) as: F(S₁,S₂,S₃)=

$\begin{matrix}{\begin{bmatrix}s_{1} & {- s_{2}^{*}} & {- s_{3}^{*}} & s_{4} & s_{5} & {- s_{7}^{*}} & {- s_{8}^{*}} & s_{6} & s_{9} & {- s_{12}^{*}} & {- s_{10}^{*}} & s_{11} \\s_{2} & s_{1}^{*} & {- s_{4}^{*}} & {- s_{3}} & s_{6} & s_{8}^{*} & s_{7}^{*} & s_{5} & s_{10} & {- s_{11}^{*}} & s_{9}^{*} & {- s_{12}} \\s_{3} & {- s_{4}^{*}} & s_{1}^{*} & {- s_{2}} & s_{7} & s_{5}^{*} & {- s_{6}^{*}} & {- s_{8}} & s_{11} & s_{10}^{*} & s_{12}^{*} & s_{9} \\s_{4} & s_{3}^{*} & s_{2}^{*} & s_{1} & s_{8} & {- s_{6}^{*}} & s_{5}^{*} & {- s_{7}} & s_{12} & s_{9}^{*} & {- s_{11}^{*}} & {- s_{10}}\end{bmatrix}.} & (12)\end{matrix}$

As the EQO-STBC has unity code rate, with a coding block length of 12symbols in this case, it can effectively increase the randomization ofFEC (Forward Error Correction) code words, and therefore improve systemperformance. This is preferably achieved in conjunction with effectivechannel interleaving to randomize any error burst.

QO-STBC and EQO-STBC discussed above can be effectively decoded by asimple linear MMSE (Minimum Mean Squared Error) decoder at a receiver,for example, for all receive antenna configurations based on MISO(Multiple Input Single Output) decoding for a single receive antenna. Anincrease of the number of receiving antennas in this case essentiallyallows an increase in power efficiency. However, if the number ofreceiving antennas is greater than 1, EQO-STBC becomes ineffective froma spectral efficiency point of view. Methods of puncturing may be usedto increase the spectral efficiency. Puncturing may be provided, forexample, by a puncturer implemented within the encoder 12 or as aseparate component of the transmitter 10. In one embodiment, theeffective decoding of EQO-STBC may be carried out with an MMSE receivereven at a reduction of half a block length for N=2 receiving antennas.One possible puncturing pattern yields the following Punctured EQO-STBC(PEQO-STBC) coding matrix from the basic mother EQO-STBC coding matrixin equation (12) above:

$\begin{matrix}{{F\left( {S_{1},S_{2},S_{3}} \right)} = {\begin{bmatrix}s_{1} & {- s_{2}^{*}} & s_{5} & {- s_{7}^{*}} & s_{9} & {- s_{12}^{*}} \\s_{2} & s_{1}^{*} & s_{6} & s_{8}^{*} & s_{10} & {- s_{11}^{*}} \\s_{3} & {- s_{4}^{*}} & s_{7} & s_{5}^{*} & s_{11} & s_{10}^{*} \\s_{4} & s_{3}^{*} & s_{8} & {- s_{6}^{*}} & s_{12} & s_{9}^{*}\end{bmatrix}.}} & (13)\end{matrix}$

The coding rate for this particular PEQO-STBC is 2, as 12 symbols aretransmitted in 6 time slots. Such a code can be used for a 4×2 antennaconfiguration for instance, with twice higher spectral efficiency thanthe 4×1 antenna configuration for EQO-STBC.

Further increasing the number of receiving antennas allows morepuncturing, and for a 4×4 antenna configuration, we have the well knownBLAST coding matrix

$\begin{matrix}{{F\left( {S_{1},S_{2},S_{3}} \right)} = \begin{bmatrix}s_{1} & s_{5} & s_{9} \\s_{2} & s_{6} & s_{10} \\s_{3} & s_{7} & s_{11} \\s_{4} & s_{8} & s_{12}\end{bmatrix}} & (14)\end{matrix}$

Of course, those skilled in the art will appreciate that differentpuncturing patterns may be used to yield different PEQO-STBC matricesfrom the same mother coding matrix. It should be noted that all threetypes of constructed codes, namely EQO-STBC, PEQO-STBC and BLAST canconstitute three adaptive space time coding modes based on the number ofreceive antennas. A particular space-time coding mode may then beselected based on communication channel conditions, for example, andvaried adaptively as conditions change. The receiver 22 has a universalreceiver structure for all these three modes, preferably including anMMSE decoder as the decoder 28, and possibly other common receivercomponents such as a soft de-mapper and a turbo decoder.

FIG. 2 is a flow diagram illustrating a method 30 according to anembodiment of the invention. A space-time coding matrix is determined at32, by generating a coding matrix or selecting from a number ofgenerated or stored coding matrices, for example. Coding matrices may bepreviously determined, either internally by an encoder or externally bya separate transmitter component or even a remote component, and storedfor later selection and use during encoding of symbols at 34.

Operations at 32 may involve generating a mother coding matrix and thenpuncturing the mother coding matrix to a desired code rate. Thus,although three unity code rate coding matrices have been describedabove, coding matrices may be generated and punctured up to unity coderate, or higher code rates. Puncturing may also be used to provideadaptive coding, wherein at least one of a puncturing ratio andpuncturing pattern is changed, based on communication channel conditionsfor instance.

Symbols, received from communication circuitry at a transmitter forexample, are encoded at 34 using the coding matrix determined at 32. Theencoded symbols may be transmitted after encoding at 34 or stored forlater transmission. Of course, encoded symbols may also be furtherprocessed by communication circuitry before transmission.

The present invention is in no way restricted to the particular methodshown in FIG. 2. As described above, further operations such aspuncturing may be performed. In addition, a coding matrix may begenerated or selected before symbols are received for encoding at 34. Ina preferred embodiment, one or more mother coding matrices, such as thematrices F⁽¹⁾ through F⁽³⁾ above, are generated and stored in memory ata transmitter for later use as QO-STBC matrices or to generate EQO-STBCor PEQO-STBC matrices, which may also be stored for later use. It willtherefore be apparent that methods according to embodiments of theinvention may perform the steps of FIG. 2 in a different order, and mayinclude fewer or further steps than those explicitly shown.

One conventional coding technique employs an orthonormal 2×2 STBC matrixthat provides for diversity order of 2 with two transmit antennas andtwo receive antennas is known. From a wireless communication networkdesign point of view, 2^(nd) order diversity improves the networkcapacity or user bit rate significantly. However, to achieve 2^(nd)order diversity, in general, this type of technique requires that tworeceive antennas be implemented at a receiver. In the case of acommunication terminal, also commonly referred to as a UE (userequipment) or an MS (mobile station), physical size and interferenceconstraints complicate the adoption of two receive antennas. Generally,it is highly desirable to use multiple antennas at a communicationnetwork element such as a base station and a single antenna at eachcommunication terminal, to provide a 4×1 system, for example.

This was a primary motivation for 3GPP to launch a transmit diversitystudy for more than two transmit antennas. Two of the most widely knownproposed schemes include so-called D-STTD (Double STTD) with a 4×2configuration and STTD-OTD with 4×1 configuration and to achieve 2^(nd)order diversity gain.

In the case of D-STTD with a 4×2 antenna configuration and the followingcoding matrix

$\begin{matrix}{{{F\left( S_{1} \right)} = \begin{bmatrix}s_{1} & {- s_{2}^{*}} \\s_{2} & s_{1}^{*} \\s_{3} & {- s_{4}^{*}} \\s_{4} & s_{3}^{*}\end{bmatrix}},} & (15)\end{matrix}$

the correlation matrix can be written as:

$\begin{matrix}{{{R = \begin{bmatrix}d_{12} & 0 & 0 & 0 & e & {- f} & {- a} & {- g} \\0 & d_{12} & 0 & 0 & f & e & g & {- a} \\0 & 0 & d_{12} & 0 & a & {- g} & {- e} & f \\0 & 0 & 0 & d_{12} & g & a & {- f} & {- e} \\e & f & a & g & d_{34} & 0 & 0 & 0 \\{- f} & e & {- g} & a & 0 & d_{34} & 0 & 0 \\{- a} & g & {- e} & {- f} & 0 & 0 & d_{34} & 0 \\{- g} & {- a} & f & {- e} & 0 & 0 & 0 & d_{34}\end{bmatrix}},{where},{{d_{1,2} = {\sum\limits_{n = 1}^{N}{\sum\limits_{{m = 1},2}^{\;}{h_{m,n}}^{2}}}};}}{{d_{3,4} = {\sum\limits_{n = 1}^{N}{\sum\limits_{{m = 3},4}^{\;}{h_{m,n}}^{2}}}};}{{a = {\sum\limits_{n = 1}^{N}{{Re}\left\{ {{h_{2,n}h_{3,n}^{*}} - {h_{1,n}h_{4,n}^{*}}} \right\}}}};}{{e = {\sum\limits_{n = 1}^{N}{{Re}\left\{ {{h_{1,n}h_{3,n}^{*}} + {h_{2,n}h_{4,n}^{*}}} \right\}}}};}{{f = {\sum\limits_{n = 1}^{N}{{Re}\left\{ {{{- h_{1,n}}h_{3,n}^{*}} + {h_{2,n}h_{4,n}^{*}}} \right\}}}};{and}}g = {\sum\limits_{n = 1}^{N}{{Re}{\left\{ {{{- h_{2,n}}h_{3,n}^{*}} - {h_{1,n}h_{4,n}^{*}}} \right\}.}}}} & (16)\end{matrix}$

It will be apparent to those skilled in the art that the diagonalelements of this matrix are proportional to the power of two symbolsonly, represented by channel factors h_(m,n), and that each of them hasa central χ² distribution with 8 degrees of freedom. With thisconfiguration, 6 other diagonal values are also possible, each beingproportional to the power of other pairs of symbols and having χ²central distribution with 8 degrees of freedom.

In accordance with another aspect of the invention, a version of codingis determined at which all 8 values are present in one correlationmatrix. Such a scheme is possible, for example, where different codingschemes are used for real and imaginary parts of complex symbols. Thefollowing coding matrix represents a version of partial optimizedNon-Orthonormal STTD determined according to one embodiment of theinvention:

$\begin{matrix}{{{F\left( S_{1} \right)} = {{{{Re}\left\{ \begin{bmatrix}s_{1} & s_{2} \\{- s_{2}^{*}} & s_{1}^{*} \\s_{3} & s_{4} \\{- s_{4}^{*}} & s_{3}^{*}\end{bmatrix} \right\}} + {j\; {Im}\left\{ \begin{bmatrix}s_{1} & s_{2} \\{- s_{2}^{*}} & s_{1}^{*} \\s_{3} & s_{4} \\{- s_{4}^{*}} & s_{3}^{*}\end{bmatrix} \right\}}} = \begin{bmatrix}s_{1} & {{{Re}\left\{ s_{2} \right\}} + {j\; {Im}\left\{ s_{3} \right\}}} \\s_{2} & {{{Re}\left\{ {- s_{3}} \right\}} + {j\; {Im}\left\{ {- s_{4}} \right\}}} \\s_{3} & {{{Re}\left\{ {- s_{4}} \right\}} + {j\; {Im}\left\{ {- s_{1}} \right\}}} \\s_{4} & {{{Re}\left\{ {- s_{1}} \right\}} + {j\; {Im}\left\{ s_{2} \right\}}}\end{bmatrix}}},} & (17)\end{matrix}$

with the correlation matrix

$\begin{matrix}{R = {\quad{\begin{bmatrix}{{\overset{\_}{h}}_{1}^{2} + {\overset{\_}{h}}_{4}^{2}} & * & * & * & * & * & * & * \\* & {{\overset{\_}{h}}_{1}^{2} + {\overset{\_}{h}}_{3}^{2}} & * & * & * & 0 & * & * \\* & * & {{\overset{\_}{h}}_{2}^{2} + {\overset{\_}{h}}_{1}^{2}} & * & * & * & * & * \\* & * & * & {{\overset{\_}{h}}_{2}^{2} + {\overset{\_}{h}}_{4}^{2}} & * & * & * & 0 \\0 & * & * & * & {{\overset{\_}{h}}_{3}^{2} + {\overset{\_}{h}}_{2}^{2}} & * & * & * \\* & * & * & * & * & {{\overset{\_}{h}}_{3}^{2} + {\overset{\_}{h}}_{1}^{2}} & * & * \\* & * & 0 & * & * & * & {{\overset{\_}{h}}_{4}^{2} + {\overset{\_}{h}}_{3}^{2}} & * \\* & * & * & * & * & * & * & {{\overset{\_}{h}}_{4}^{2} + {\overset{\_}{h}}_{2}^{2}}\end{bmatrix},\mspace{79mu} {{{{where}\mspace{14mu} {\overset{\_}{h}}_{k}^{2}} = {\sum\limits_{n = 1}^{\;}{h_{k,n}}^{2}}};}}}} & (18)\end{matrix}$

and * represents non-zero elements,The calculation of the non-zero elements will be apparent to thoseskilled in the art, and as such, the values are not explicitly specifiedherein for brevity,

It can be seen that the diagonal elements of the above correlationmatrix contain all of the possible combinations of channel matrixelements, and that a large number of non-zero correlation coefficientsis also introduced. This coding scheme is referred to herein primarilyas Randomised Non-Orthonormal STBC (RNO-STBC), with a coding rate of 2in the above example. Whereas embodiments of QO-STBC as described aboveare designed to minimize a number of non-zero correlation coefficients,which are off-diagonal elements of a correlation matrix associated withan QO-STBC coding matrix, RNO-STBC is designed to increase or enhance,and preferably maximize, the power of a trace of the correlation matrix.

FIG. 3 is a plot of FER versus Eb/No for simulations of embodiments ofthe invention and an example 4×2 communication scheme. It should beappreciated that the plot of FIG. 3 is presented solely for the purposeof illustration, and that the invention is in no way limited to thesimulation conditions listed at the top of FIG. 3. The frame lengthL=1280 is one illustrative example frame length, rate R=½ Turbo codingrepresents further processing that may be performed on symbols before orafter space-time encoding, and modulation by QPSK is an example of atechnique for generating data symbols. Similarly, an MMSE receiver isone example of a type of receiver in conjunction with which symbolsencoded according to embodiments of the invention may be decoded. Othersuitable types of receiver may be apparent to those skilled in the art.

As can be seen from the simulation results in FIG. 3, RNO-STBCoutperforms D-STTD, providing approximately a 1 dB gain thereover at anFER of about 1.00E-02, and PEQO-STBC outperforms both RNO-STBC andD-STTD. As shown, PEQO-STBC provides approximately 2dB gain over D-STTDfor the simulation conditions at an FER of about 1.00E-02.

The simulation results of FIG. 3 correspond to a 4×2 antennaconfiguration. The techniques described above are also applicable to 4×1configurations, as well as others. Those skilled in the art willappreciate that STTD-OTD for an illustrative example 4×1 configurationis similar to D-STTD, with a coding matrix

$\begin{matrix}{{F\left( S_{1} \right)} = {\begin{bmatrix}s_{1} & s_{1} & s_{2} & s_{2} \\{- s_{2}^{*}} & {- s_{2}^{*}} & s_{1}^{*} & s_{1}^{*} \\s_{3} & s_{3} & s_{4} & s_{4} \\{- s_{4}^{*}} & {- s_{4}^{*}} & s_{3}^{*} & s_{3}^{*}\end{bmatrix}.}} & (19)\end{matrix}$

FIGS. 4 and 5 are plots of FER versus Eb/No for simulations ofembodiments of the invention and an example 4×1 communication scheme. Asdescribed above in conjunction with FIG. 3, it should be appreciatedthat the plots of FIGS. 4 and 5 are presented for illustrative purposes,and that the invention is in no way limited to these particularsimulation conditions, with Turbo coding and modulation by QPSK (FIG. 4)or 64 QAM (FIG. 5).

In both FIGS. 4 and 5, QO-STBC outperforms STTD-OTD, and EQO-STBCoutperforms QO -STBC, providing an approximate 1 dB gain over STTD-OTDat an FER of about 1.00E-02.

Referring again to the above QO-STBC coding matrices, the correlationfactors in the corresponding correlation matrices are defined only byone value. For example, for the first QO-STBC matrix F⁽¹⁾ withcorrelation matrix R⁽¹⁾, we have

|R _(k,m)|=2|Re{h ₁ h ₄ *−h ₂ h ₃*}|  (20)

where (k,m)∈{(1_(r),4_(r)), (1_(i),4_(i)),(2_(r),3_(r)),(2_(i),3_(i))}.}Introducing a phase rotation factor for the first and secondtransmitting antennas as

Θ_(1,2)=exp(jθ _(1,2)),   (21)

the correlation factor, with this phase rotating factor, becomes

|R _(m,n)|=2|Re{Θ _(1,2)(h ₁ h ₄ *−h ₂ h ₃*)}|.   (22)

If the phase angle of the phase rotating factor is calculated as

θ_(1,2)=−arg(h ₁ h ₄ *−h ₂ h ₃*)+π/2,   (23)

then all correlation factors will be equal to zero. If the number ofreceiving antennas is more than one, then the following similar rule maybe defined for the correction phase rotation:

$\begin{matrix}{\theta_{1,2} = {{{- \arg}\left\{ {\sum\limits_{n = 1}^{N}\left( {{h_{1,n}h_{4,n}^{*}} - {h_{2,n}h_{3,n}^{*}}} \right)} \right\}} + {\pi/2.}}} & (24)\end{matrix}$

Thus, by tuning of phases of both first and second transmitting antennaswith the same value, according to an embodiment of the invention, it ispossible to orthonormalize the covariance matrix of STBC coding. In thiscase, diversity gain will be maximum, equal to 4 for a 4×1 system.

Similarly, for the second type of QO-STBC matrix above, we have

|R _(m,n)|=2|Re{h ₁ h ₂ *-31 h ₃ h ₄*}|.   (25 )

For this type of QO-STBC, the phases of the first and third transmittingantennas are preferably tuned with the phase angle

θ_(1,3)=−arg(h ₁ h ₂ *−h ₃ h ₄*)+π/2.   (26)

For the third type of QO-STBC matrix,

|R _(m,n)|=2|Re{h ₁ h ₃ *−h ₂ h ₄*}|,   (27)

and the phases of first and fourth transmitting antennas are preferablytuned using the phase angle

θ_(1,4)=−arg(h ₁ h ₃ *″h ₂ h ₄*)+π/2.   (28)

As the above phase angles are dependent only upon channelcharacteristics, these phase angles may also be used for tuning antennaswhere permutations or punctured versions of F⁽¹⁾, F⁽²⁾ and F⁽³⁾ areused.

FIG. 6 is a block diagram of a closed loop system according to anembodiment of the invention. The example closed loop system of FIG. 6includes a transmitter 40, and a receiver 42. The transmitter 40includes a space-time encoder 44, connected to M=4 antennas 46, 48, 50,52, complex multipliers 54, 56 connected in a signal path between theencoder 44 and the first two antennas 46, 48, and a phasor 58 connectedto the complex multipliers 54, 56. The receiver 42 includes an antenna60 connected to a decoder 62, which is connected to a phase angleestimator 64. Although a separate feedback channel between the receiver42 and the transmitter 40 has been explicitly shown in FIG. 6, thoseskilled in the art will appreciate that such a channel is preferablyprovided as a wireless communication channel, such that feedbackinformation described in further detail below is fed back to thetransmitter 40 by the receiver 42 via the antenna 60. As above, thetransmitter 40 and the receiver 42 may include further or differentcomponents than those explicitly shown in FIG. 6.

In the transmitter 40, the encoder 44 and the antennas 46, 48, 50, 52operate substantially as described above to encode and transmit symbolsto the receiver 42. The decoder 62 decodes symbols received by theantenna 60.

In accordance with an embodiment of the invention, a phase angle of aphase rotation factor is determined by the phase angle estimator 64based on communication channel gain factors, as described above. In apreferred embodiment, feedback information includes a single real numberwhich is independent of the number of receive antennas, I in FIG. 6. Anestimated phase angle can be quantized, for example, with the choice ofthe following three set of values for 1-, 2-, and 3-bit feedback:

-   -   1-bit feedback:

$\left\{ {0,\frac{\pi}{2}} \right\}$

-   -   2-bit feedback:

$\left\{ {0,\frac{\pi}{4},\frac{\pi}{2},\frac{3\; \pi}{4}} \right\}$

-   -   3-bit feedback:

$\left\{ {0,\frac{\pi}{8},\frac{\pi}{4},\frac{3\; \pi}{8},\frac{\pi}{2},\frac{5\; \pi}{8},\frac{3\; \pi}{4},\frac{7\; \pi}{8}} \right\}.$

Other numbers of feedback bits, quantization step sizes, andquantization levels may also be used.

The feedback information is received at the transmitter 40 andtranslated into a phase angle by the phasor 58, using the appropriatemapping above for 1-, 2-, or 3-bit feedback for instance. A phaserotation factor is then determined applied to the signals output to thefirst two antennas 46, 48 by the complex multipliers 54, 56. The complexmultipliers 54, 56 are examples of phase shifters and may be replacedwith other types of phase shifters in alternate embodiments of theinvention.

The system of FIG. 6 represents one illustrative embodiment of a closedloop system. It should be appreciated that the invention is in no waylimited thereto.

For example, the system of FIG. 6 provides for phase rotation at thefirst and second antennas 46, 48, and thus correspond to the first typeof QO-STBC matrix above. Systems for the second and third types ofQO-STBC matrices will be substantially similar, with the complexmultipliers 54, 56 connected in different combinations of the signalpaths between the encoder 44 and the antennas 46, 48, 50, 52. Where thefunction of the complex multipliers 54, 56 is implemented in software, aphase rotation factor may be applied to any combination of the signalpaths using substantially the same transmitter.

In addition, the system of FIG. 6 shows feedback of information from thereceiver 42 to the transmitter 40. If the transmitter 40 is able todetermine channel gain factors, then the determination of a phase anglemay be performed at the transmitter 40. Similarly, although the receiver42 incorporates the phase angle estimator 64 in FIG. 6, a receiver mayinstead feed back channel gain information to a transmitter for use bythe transmitter in determining a phase angle, or determine and feed backa phase rotation factor to be applied at the transmitter 40. In theformer case, more feedback information is transmitted by the receiver,but calculation of the phase angle is off-loaded to the transmitter.Thus, it will be apparent that the receiver 42 may feed back a phaserotation factor or information to be used at the transmitter 40 indetermining a phase rotation factor.

As described above, different phase angles may be used for differentcoding matrices. In a preferred embodiment for receiver feedback, thereceiver 42 is configured for operation with a particular type ofQO-STBC matrix and is adapted to determine corresponding feedbackinformation. According to other embodiments, the transmitter 40 providesan indication of coding matrix type to the receiver 42. Alternatively,the receiver 42 determines feedback information associated with aplurality of coding matrices and either selects and transmits onlyparticular feedback information for a specific coding matrix, ortransmits the feedback information to the transmitter 40, which thenselects particular feedback information for a coding matrix.

FIG. 7 is a flow diagram of a closed loop method 70 according to anembodiment of the invention. At 72 and 74, a coding matrix is determinedand used to encode symbols, substantially as described above. A phaserotation factor is determined at 76, by a receiver of the encodedsymbols in one embodiment of the invention. Encoded symbols are thenrotated using the phase rotation factor at 78. The phase rotation factoris preferably determined such that the rotation at 78 forcesoff-diagonal correlation factors in a correlation matrix of the codingmatrix to zero.

Consider now a possible combination of QO-STBC with closed loop controlfor a 4×2 configuration. In this case, it is possible to use PuncturedQO-STBC, by further puncturing the QO-STBC. For the first type ofQO-STBC above, after puncturing we have

$\begin{matrix}{{{F\left( S_{1} \right)} = \begin{bmatrix}s_{1} & {- s_{2}^{*}} \\s_{2} & s_{1}^{*} \\s_{3} & {- s_{4}^{*}} \\s_{4} & s_{3}^{*}\end{bmatrix}},} & (29)\end{matrix}$

which is the same as D-STTD. The correlation matrix, as given above butwith slightly different notation, is

$\begin{matrix}{{{{{R = \begin{bmatrix}{A + B} & 0 & 0 & 0 & {G + Q} & {{- H} + P} & {K - M} & {{- L} - N} \\0 & {A + B} & 0 & 0 & {H - P} & {G + Q} & {L + N} & {K - M} \\0 & 0 & {B + A} & 0 & {M - K} & {{- N} - L} & {{- Q} - G} & {{- P} + H} \\0 & 0 & 0 & {B + A} & {N + L} & {M - K} & {P - H} & {{- Q} - G} \\{G + Q} & {H - P} & {M - K} & {N + L} & {C + D} & 0 & 0 & 0 \\{{- H} + P} & {G + Q} & {{- N} - L} & {M - K} & 0 & {C + D} & 0 & 0 \\{K - M} & {L + N} & {{- Q} - G} & {P - H} & 0 & 0 & {D + C} & 0 \\{{- L} - N} & {K - M} & {{- P} + H} & {{- Q} - G} & 0 & 0 & 0 & {D + C}\end{bmatrix}},\mspace{79mu} {where}}\mspace{79mu} {{A = {h_{1,r}^{2} + h_{1,i}^{2}}};}\mspace{79mu} {{B = {h_{2,r}^{2} + h_{2,i}^{2}}};}\mspace{79mu} {{C = {h_{3,r}^{2} + h_{3,i}^{2}}};}\mspace{79mu} {{D = {h_{4,r}^{2} + h_{4,i}^{2}}};}\mspace{85mu} {{G = {{h_{1,r}h_{3,r}} + {h_{1,i}h_{3,i}}}};}\mspace{79mu} {{H = {{{- h_{1,i}}h_{3,r}} + {h_{1,r}h_{3,i}}}};}\mspace{79mu} {{K = {{h_{1,r}h_{4,r}} + {h_{1,i}h_{4,i}}}};}\mspace{79mu} {{L = {{{- h_{1,i}}h_{4,r}} + {h_{1,r}h_{4,i}}}};}\mspace{79mu} {M = {{h_{2,r}h_{3,r}} + {h_{2,i}h_{3,i}}}}};}\mspace{79mu} {{N = {{{- h_{2,i}}h_{3,r}} + {h_{2,r}h_{3,i}}}};}\mspace{79mu} {{Q = {{h_{2,r}h_{4,r}} + {h_{2,i}h_{4,i}}}};{and}}\mspace{79mu} {P = {{{- h_{2,i}}h_{4,r}} + {h_{2,r}{h_{4,i}.}}}}} & (30)\end{matrix}$

The total power of correlation peaks with several receive antennas willbe

$\begin{matrix}{\begin{matrix}{{\sum R^{2}} = {\left( {G + Q} \right)^{2} + \left( {H - P} \right)^{2} + \left( {M - K} \right)^{2} + \left( {N + L} \right)^{2}}} \\{= {{{H_{31} + H_{24}}}^{2} + {{H_{32} - H_{14}}}^{2}}}\end{matrix}{where}{{H_{13} = {\sum\limits_{n = 1}^{N}{h_{1,n}h_{3,n}^{*}}}};}{{H_{24} = {\sum\limits_{n = 1}^{N}{h_{2,n}h_{4,n}^{*}}}};}{{H_{32} = {\sum\limits_{n = 1}^{N}{h_{3,n}h_{2,n}^{*}}}};{and}}{H_{14} = {\sum\limits_{n = 1}^{N}{h_{1,n}{h_{4,n}^{*}.}}}}} & (31)\end{matrix}$

With the above common rotating factor θ_(1,2)=exp(jθ_(1,2)) for both thefirst and second transmitting antennas, the total power of correlationpeaks will be depend on the phase of rotating factor, as follows:

ΣR(θ_(1,2))² =|H ₃₁ exp(−jθ _(1,2))+H ₂₄ exp(jθ _(1,2))|² +|H ₃₂ exp(−jθ_(1,2))−H ₁₄ exp(jθ _(1,2))|²   (32)

It can be shown that such a total power of correlation peaks has aminimum value with respect to certain rotation phase θ_(1,2). Thus,based on phase tuning of the first and second transmitting antennas withthe phase θ_(1,2), it is possible to reduce the total level ofcorrelation peaks of an STBC transformation for a 4×2 configuration.From the foregoing description of phase angle determination, derivationof corresponding phase angle values for this embodiment will be apparentto those skilled in the art.

FIG. 8 is a plot of FER versus Eb/No for simulations of closed loopembodiments of the invention and an example conventional closed loopcommunication scheme. As shown, for the particular simulation conditionsindicated at the top of FIG. 8, to which the invention is in no waylimited, 1-bit feedback, indicated by QO-STBC(CL), provides anapproximate gain of 1.5 dB over the closed loop D-STTD scheme at an FERof about 1.00E-02. 2-, 4-, and 8-bit feedback, indicated by CL2, CL4,and CL8, respectively, provide an approximate gain of 2 dB over closedloop D-STTD at the same FER.

FIG. 9 is a plot of FER versus Eb/No for simulations of open loop andclosed loop embodiments of the invention. In this case, for the listedsimulation conditions, 1-bit feedback provides approximately 0.75 dBgain, and 2-, 4-, and 8-bit feedback provide a higher gain ofapproximately 1.5 dB at an FER of about 1.00E-02.

For all of the simulation results presented herein, it should beappreciated that simulation conditions are intended for illustrativepurposes only, and that the invention is in no way limited thereto.Also, simulation results are expected to vary from those shown fordifferent simulation conditions,

FIGS. 10 and 11 are block diagrams of embodiments of the inventionadapted for CDMA communication systems. In FIG. 10, outputs of aspace-time encoder 80 are connected to complex multipliers 82, 84, 86,88, which are connected to antennas 96, 98, 100, 102. Delay stages 90,92 are connected in signal paths between the encoder 80 and themultipliers 86, 88 to delay encoded symbols. The delay stage 94similarly delays a scrambling code which is retrieved from memory forinstance.

In operation, scrambling codes are applied to encoded symbols from theencoder 80, which have been encoded using a space-time coding matrix asdescribed above, in the complex multipliers 82, 84, 86, 88. The delaystages 90, 92, 94 create additional delayed versions of the signals asartificial multipath signals. Generation of such multipath signals canbe considered a form of space time coding, and as such, the multipathsignals may therefore be separated and combined by a space time decoder.

The system of FIG. 11, which is an alternative realization of a 4transmit antenna QO-STTD scheme, includes a plurality of encoders 104,106, 108, 110, having inputs connected to receive symbols to betransmitted and outputs connected to complex multipliers 112, 114, 116,118. The complex multipliers are connected to signal combiners,illustratively adders 120 122, 124. The outputs of the adders 124 areconnected to antennas 126, 128, 130, 132. The delay stages 134, 136, 138delay the scrambling code for input to the complex multipliers 114, 116,118.

The operation of the system of FIG. 11 is similar to the system of FIG.10, in that a scrambling code is applied to encoded symbols output fromthe encoders 104, 106, 108, 110 by the complex multipliers 112, 114,116, 118. However, in FIG. 11, the space and time aspects of space-timecoding are separated. Each of the encoders 104, 106, 108, 110effectively encodes input symbols using respective columns of aspace-coding matrix. Thus, symbols for transmission during a first timeslot are encoded by the encoder 104, and symbols for subsequentrespective time slots are encoded by the encoders 106, 108, 110. Each ofthe delay stages 134, 136, 138 delays the scrambling code by one timeslot, such that the scrambling code is aligned with the symbols for acorresponding time slot.

What has been described is merely illustrative of the application of theprinciples of the invention. Other arrangements and methods can beimplemented by those skilled in the art without departing from thespirit and scope of the present invention.

For example, although embodiments of the invention have been describedabove primarily in the context of symbols, illustratively QPSK or QAMsymbols, the invention is in no way limited thereto. A symbol includesnot only such modulation symbols, but also other types of portions,sections, or processed versions of information to be transmitted.

In addition, embodiments of the invention may be implemented inconjunction with many different frame and time slot structures.According to a preferred embodiment, a coding scheme is adapted for aframe and slot structure compatible with HSDPA (High Speed DownlinkPacket Access).

1. A method comprising: determining a plurality of space-time codingmatrices, each having a respective associated correlation matrixcomprising a plurality of non-zero off-diagonal elements; selecting oneof the plurality of space-time coding matrices for which the associatedcorrelation matrix has a least number of non-zero off-diagonal elements;encoding data symbols using the selected space-time coding matrix,determining a phase rotation factor, wherein the phase rotation factoris determined to reduce values of the off-diagonal elements of thecorrelation matrix associated with the selected space-time codingmatrix, wherein determining a phase rotation factor comprises receivingthe phase rotation factor from a receiver to which the data symbols areto be transmitted, and, applying the phase rotation factor to theencoded data symbols.
 2. The method of claim 1, further comprising:puncturing the selected space-time coding matrix, wherein encodingcomprises encoding the data symbols using the punctured selectedspace-time coding matrix.
 3. The method of claim 1, wherein determininga phase rotation factor comprises:receiving feedback information from areceiver to which the data symbols are to be transmitted; andcalculating the phase rotation factor based on the feedback information.4. The method of claim 3, wherein the feedback information comprises acode representing a phase angle for the phase rotation factor determinedon the basis of communication channel gain factors.
 5. The method ofclaim 4, wherein the code has a length selected from the groupconsisting of: 1 bit, 2 bits, and 4 bits.
 6. The method of claim 1,further comprising: transmitting the encoded data symbols from atransmitter to a receiver; receiving the encoded data symbols at thereceiver; decoding the received encoded data symbols; determiningfeedback information at the receiver; transmitting the feedbackinformation to the transmitter; receiving the feedback information atthe transmitter; and determining a phase rotation factor at thetransmitter based on the received feedback information for use inencoding subsequent data symbols.
 7. The method of claim 1, furthercomprising: transmitting the encoded data symbols from a transmitter toa receiver; receiving the encoded data symbols at the receiver; decodingthe received encoded data symbols; determining the phase angle θ of thephase rotation factor at the receiver; and transmitting the phase angleθ to the transmitter.
 8. A method comprising: receiving a communicationsignal comprising data symbols encoded using a space-time coding matrixselected from a plurality of space-time coding matrices havingrespective associated correlation matrices comprising a plurality ofnon-zero off-diagonal elements, the associated correlation matrix forthe selected space-time coding matrix having a least number of non-zerooff-diagonal elements; decoding the encoded data symbols; determiningfeedback information, wherein the feedback information comprises a phaseangle for a phase rotation factor to be applied to the subsequent datasymbols to reduce values of the off-diagonal elements of the correlationmatrix associated with the selected space-time coding matrix; andtransmitting the feedback information to a transmitter of thecommunication signal for use in encoding subsequent data symbols.
 9. Themethod of claim 8, wherein the feedback information comprises a coderepresenting the phase angle.
 10. The method of claim 8, whereindetermining comprises: determining communication channel gain factors;and determining the phase angle based on the communication channel gainfactors.
 11. The method of claim 8, wherein the feedback informationcomprises communication channel gain factors for use in calculating aphase rotation factor to be applied to the subsequent data symbols toreduce values of the off-diagonal elements of the correlation matrix.12. A system comprising: an input configured to receive data symbols;and a processor configured to determine a plurality of space-time codingmatrices, each having a respective associated correlation matrixcomprising a plurality of non-zero off-diagonal elements, to select oneof the plurality of space-time coding matrices for which the associatedcorrelation matrix has a least number of non-zero off-diagonal elements,to encode the data symbols using the selected space-time coding matrix,to determine a phase rotation factor, wherein the phase rotation factoris determined to reduce values of the off-diagonal elements of thecorrelation matrix associated with the selected space-time codingmatrix, and to apply the phase rotation factor to the encoded datasymbols, wherein the input is further configured to receive feedbackinformation from a receiver to which the data symbols are to betransmitted, and wherein the processor is further configured tocalculate the phase rotation factor based on the feedback information.13. The system of claim 12, wherein the feedback information comprises acode representing a phase angle for the phase rotation factor determinedon the basis of communication channel gain factors.
 14. The system ofclaim 12, wherein the processor implements a phasor for converting thecode to the phase rotation factor.
 15. The system of claim 12, furthercomprising: a plurality of multipliers for applying a scrambling code torespective ones of the encoded data symbols; and a plurality of delaystages connected to at least one of the multipliers for delaying theencoded symbol and the scrambling code for the at least one of themultipliers.